teaching, math, teaching math

Answering Questions

We must not fool ourselves, as for years I fooled myself, into thinking that guiding children to answers by carefully chosen leading questions is in any important respect different from just telling them the answers in the first place. Children who have been led up to answers by teachers’ questions are later helpless unless they can remember the questions, or ask themselves similar questions, and this is exactly what they cannot do. The only answer that really sticks in a child’s mind is the answer to a question that he asked or might ask of himself (199).

-John Holt, How Children Fail

I had a long stage of teaching where I avoided, as much as possible, answering student questions. I came across the article “Never Say Anything a Kid Can Say”, and it became a dogma for me. When a student asked a question, I would either ask them some clever leading questions to lead them to the answer, or (more often) tell them to “use their resources” or “figure it out”.

This didn’t work particularly well. Some kids were able to figure things out, but I left many more floundering, and created classroom management problems in the process. And it was the kids who were already struggling who benefited the least from this strategy, falling even further behind.

At some point I realized that this wasn’t working particularly well, but I still didn’t want to answer every question a student asked. My criteria became arbitrary; I met some student questions with my own questions, but I might answer a question if I was frustrated or the lesson wasn’t going as well as I wanted. I built up some intuition over time for what questions I thought I should answer and what questions I shouldn’t, but it was haphazard and I’m skeptical my questioning was particularly effective.

Students only ask three types of questions: (1) proximity questions–asked when the teacher is close; (2) stop-thinking questions–most often of the form ‘is this right’l and (3) keep-thinking questions–questions that students ask so they can get back to work. Only the third of these types should be answered. The first two types need to be acknowledged but not answered (382).

I’m still sorting through what Liljedahl means by (1) and (2), but I want to focus on (3).

The idea of a “keep-thinking” question seems like a useful and practical criterion for answering questions. Will the answer to the question allow the student to keep doing mathematical thinking, or is the valuable mathematical thinking between the student and the answer they’re looking for?

When a student asks a question because they are stuck, and the answer to that question will allow them to keep thinking, that seems like a particularly useful moment for learning, and a moment where being helpful may be the best strategy.

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6 thoughts on “Answering Questions”

Dylan
This reminds me of one of my favorite conversations with a student. I had a group of kids I worked with for four years straight (Algebra II, Precalculus, Calc AB, Calc BC) I asked one girl, named Ashley, how she felt about the upcoming Calc BC exam. She said she was not nervous at all because ‘I know if I get stuck I will hear your voice in my head asking me questions that will lead me where I need to go’ Now, we had the advantage of working together a long time and she knew my routines. This story made me proud of my questioning techniques, but I have seen too often the kind of pattern you describe where students are unable to get themselves kick started on their own. I really wrestle with this and your blog post has me thinking hard (again) about this. Thanks!

Good food for thought. Makes me wonder whether my questioning is consistent enough to do that — I would guess no. And teacher questioning is a huge rabbit hole that I’m trying to avoid in this post.

But I think, while that’s an awesome goal to aspire to, I don’t think it’s one to depend on. Not sure where that balance lies, in terms of building up consistent questioning strategies while at the same time avoiding doing the work for the student. I would like to think that this distinction, about keep-thinking questions, is a useful one in that regard but I can see the contradictions.

I think what I would say is this – I am a believer in modeling the behavior I hope that my students will develop on their own. I kind of hope this as a parent as well. Given this hope, if I can model inquisitiveness, if I can model curiosity, and if I can model being open to going down dead ends every once in a while, then there is a better chance of my students developing these habits. We can certainly debate the effectiveness of this kind of modeling – I see its limits in my children routinely. We can also debate whether these are the kind of habits that we want to develop in our students, but I want to try and make clear my goals in the kind of behavior I was describing above.
Thanks for a thought provoking post and for engaging in this conversation.

I love Jim’s idea about modeling good questions. Sometimes I respond to the first two kinds of questions with categorizing. “Oh, that’s a perfect question for your partner/group! What do you guys say?” “So good to check; how could you figure out if it’s right?” and sometimes “Are you asking how I think about it? I could share how I’d get started.”